Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces
It is known that a continuous linear operator T defined on a Banach function space X(μ) (over a finite measure space ( Omega,§igma,μ)) and with values in a Banach space X can be extended to a sort of optimal domain. Indeed, under certain assumptions on the space X(μ) and the operator T this optim...
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| Format: | Online |
| Sprog: | engelsk |
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Logos Verlag Berlin
2021
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| Online adgang: | ONIX_20210408_9783832545574_28 |
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| _version_ | 1869521764285939712 |
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| author | Blaimer, Bettina |
| author_browse | Blaimer, Bettina |
| author_facet | Blaimer, Bettina |
| author_sort | Blaimer, Bettina |
| collection | Directory of Open Access Books |
| description | It is known that a continuous linear operator T defined on a Banach function space X(μ) (over a finite measure space ( Omega,§igma,μ)) and with values in a Banach space X can be extended to a sort of optimal domain. Indeed, under certain assumptions on the space X(μ) and the operator T this optimal domain coincides with L±(mâ T), the space of all functions integrable with respect to the vector measure mâ T associated with T, and the optimal extension of T turns out to be the integration operator Iâ mâ T. In this book the idea is taken up and the corresponding theory is translated to a larger class of function spaces, namely to Fréchet function spaces X(μ) (this time over a Ï -finite measure space ( Omega,§igma,μ)). It is shown that under similar assumptions on X(μ) and T as in the case of Banach function spaces the so-called ``optimal extension process'' also works for this altered situation. In a further step the newly gained results are applied to four well-known operators defined on the Fréchet function spaces L^p-([0,1]) resp. L^p-(G) (where G is a compact Abelian group) and L^pâ textloc( mathbbR). |
| format | Online |
| id | doab-20.500.12854ir-64485 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | Logos Verlag Berlin |
| publisherStr | Logos Verlag Berlin |
| record_format | ojs |
| spelling | doab-20.500.12854ir-644852024-04-04T14:41:07Z Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces Blaimer, Bettina Optimal domain process Fréchet function spaces Vector measures thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis It is known that a continuous linear operator T defined on a Banach function space X(μ) (over a finite measure space ( Omega,§igma,μ)) and with values in a Banach space X can be extended to a sort of optimal domain. Indeed, under certain assumptions on the space X(μ) and the operator T this optimal domain coincides with L±(mâ T), the space of all functions integrable with respect to the vector measure mâ T associated with T, and the optimal extension of T turns out to be the integration operator Iâ mâ T. In this book the idea is taken up and the corresponding theory is translated to a larger class of function spaces, namely to Fréchet function spaces X(μ) (this time over a Ï -finite measure space ( Omega,§igma,μ)). It is shown that under similar assumptions on X(μ) and T as in the case of Banach function spaces the so-called ``optimal extension process'' also works for this altered situation. In a further step the newly gained results are applied to four well-known operators defined on the Fréchet function spaces L^p-([0,1]) resp. L^p-(G) (where G is a compact Abelian group) and L^pâ textloc( mathbbR). 2021-04-08T19:39:50Z 2021-04-08T19:39:50Z 2017 book ONIX_20210408_9783832545574_28 9783832545574 https://directory.doabooks.org/handle/20.500.12854/64485 eng image/jpeg Attribution-NonCommercial-NoDerivatives 4.0 International https://www.logos-verlag.de/cgi-bin/engbuchmid?isbn=4557&lng=eng&id= https://www.logos-verlag.de/ebooks/OA/978-3-8325-4557-4.pdf Logos Verlag Berlin Logos Verlag Berlin 10.30819/4557 10.30819/4557 04b263a1-7fba-4491-9eae-1c394ac42fc3 9783832545574 Logos Verlag Berlin 137 Berlin/Germany open access |
| spellingShingle | Optimal domain process Fréchet function spaces Vector measures thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis Blaimer, Bettina Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces |
| title | Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces |
| title_full | Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces |
| title_fullStr | Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces |
| title_full_unstemmed | Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces |
| title_short | Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces |
| title_sort | optimal domain and integral extension of operators acting in frechet function spaces |
| topic | Optimal domain process Fréchet function spaces Vector measures thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis |
| topic_facet | Optimal domain process Fréchet function spaces Vector measures thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis |
| url | ONIX_20210408_9783832545574_28 |
| work_keys_str_mv | AT blaimerbettina optimaldomainandintegralextensionofoperatorsactinginfrechetfunctionspaces |